Problem: Solve for $x$ and $y$ using elimination. ${-4x+3y = 1}$ ${-2x-4y = -38}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $-2$ ${-4x+3y = 1}$ $4x+8y = 76$ Add the top and bottom equations together. $11y = 77$ $\dfrac{11y}{{11}} = \dfrac{77}{{11}}$ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into $\thinspace {-4x+3y = 1}\thinspace$ to find $x$ ${-4x + 3}{(7)}{= 1}$ $-4x+21 = 1$ $-4x+21{-21} = 1{-21}$ $-4x = -20$ $\dfrac{-4x}{{-4}} = \dfrac{-20}{{-4}}$ ${x = 5}$ You can also plug ${y = 7}$ into $\thinspace {-2x-4y = -38}\thinspace$ and get the same answer for $x$ : ${-2x - 4}{(7)}{= -38}$ ${x = 5}$